1. Field of the Invention
The present invention relates in general to digital filtering. In particular, the present invention relates to a method and apparatus for determining the peak of a signal function using multiple-resolution techniques.
2. Background of the Invention
Generally, in applications such as ground-based digital cellular mobile networks, it is necessary for the fixed network to determine the location of mobiles within the system. Knowing the location of a mobile relative to a base station allows the network to coordinate handoffs of the mobile to other base stations, thereby maintaining signal strength and resolution as the mobile moves throughout the network and between cells. Typically, such systems determine location through triangulation by a group of base stations which continuously measure the time of arrival of mobiles within their cellular range. Such systems usually measure peaks in the received signal wave function and evaluate time of arrival based on those peaks.
In the past, the task of locating peaks of the signal functions has been solved by exhaustive sampling of each signal. An interpolator working within the region of interest would sample random or interval phase points in an attempt to locate the function. For example, under IS-136 digital cellular standards, the outputs of a synchronized correlation may be available with a sampling period Ts=5.144 xcexcs. When the system is attempting to locate the position of a mobile unit, the peak of this correlation function needs to be estimated to an accuracy of the order of 30 ns, to yield a range measurement to the mobile with a resolution of 9 m. The ratio of the sampling period to the desired resolution is therefore roughly 172. The standard techniques would need to interpolate the correlation function in the region of interest by a factor of 172, and then determine the maximum of the interpolated output.
Maximization of a discrete function typically requires a search procedure. In conventional techniques, this search procedure is carried out on all of the outputs of the interpolator, and essentially involves interpolating the samples the function at the desired resolution. Special cases of the implementation may include a linear, quadratic or other polynomial-fitting interpolators.
These solutions are complex, however, in that they require systems to process a large number of nonrelevant data points in an attempt to locate a relatively small number of peaks. This sacrifices speed, processing resources and power within any system that requires the detection of signal peaks. In cellular networks in particular, where large numbers of calculations on many mobile units are required, such inefficiencies translate into system bottlenecks that may affect cellular service.
To obviate one or more of the above problems due to limitations and disadvantages of the related art, the invention is a method and apparatus for determining the location of the peak of a signal function using multi-resolution techniques. The technique is useful when the desired accuracy of the estimated peak is a small fraction of the sampling period of the function.
The present invention may be embodied in a method including the steps of providing a set of calculated output points for the function using a predetermined calculation interval. A maximum output point of the set is then determined, and the output points of the function are interpolated only within the region of the maximum. A maximum of the interpolated output points approaches the peak of the function. This allows accurate detection of the peak of a function in cases where the function is available at a sampling frequency much lower than the desired resolution of the peak.
In another aspect of the invention, a method for approaching the peak of a function using at least one digital filter is provided. The digital filter operates on the function with a plurality of filtering coefficients. The method includes the steps of providing a first set of output points of the function spaced at a uniform interval and determining a first maximum output point. Output points immediately adjacent the first maximum output point are then selected so that the adjacent output points define a first phase region surrounding the first maximum output point. A second set of output points surrounding the first maximum output point along the first phase region is then sampled, and a second maximum output point of the second set of output points is determined. Adjacent output points of the second set are then selected to define a second phase region around the second maximum output point. A third set of output points is then sampled surrounding the second maximum output point along the second phase region, and a third maximum output point is determined. Through these iterations, the determined maximums begin to approach the region of the true peak. Outputs from the function are obtained by changing the filtering coefficients to sample points in varying phases.
In yet another aspect of the present invention, a method for locating the peak of a correlation function waveform is provided. The method includes the steps of loading the shift registers of the filter bank with a first set of correlations calculated at an input sampling period. A first maximum correlation value is then detected from the first set of correlations. The filter coefficients are then updated to obtain a second set of correlations which are shifted in phase from the first set of correlations. The second set of correlations have a period less than the input sampling period and are positioned adjacent to the first maximum correlation value. Finally, a second maximum correlation value is detected from the second set of correlations. This second maximum correlation value improves in approximation to the peak of the function over the first maximum correlation value previously detected.
In yet another aspect of the present invention, a method is provided for locating the peak of a correlation function using a digital filter bank. The method includes the steps of detecting a first maximum correlation value from a first set of correlations which are initially calculated at a uniform first interval. The coefficients of the filter are then changed to obtain a second set of correlations shifted in phase from the first set of correlations. This second set of correlations are spaced at a smaller second interval and exist adjacent to the first maximum correlation value. A second maximum correlation value is then detected from the second set of correlations. This second maximum begins to approach a peak of the function, and the steps of the method are then repeated to calculate iterations only within adjacent phases between progressively smaller intervals.
The invention may be further embodied in an apparatus which includes a plurality of interconnected digital filters operating on the function to calculate output values, and at least one control unit in communication with the digital filters. The control unit controls the output of the filters and selects a first maximum of the output values. The control unit allows progressive interpolation of output values surrounding the first maximum to determine whether the interpolated output values approach a peak.
The invention thus allows the location of the peak of a signal using a high resolution only within a region of interest. This approach has the advantage of reducing the complexity of the interpolative process typically used to located a maximum. By focusing only within a specified phase region, the need for exhaustive random sampling of the entire function is eliminated. Furthermore, the apparatus combining a filter bank for interpolating points in the function and a control unit for isolating interpolative maximums simplifies the hardware, power and time necessary to perform maximization calculations.
The particular embodiments discussed herein may be used in any system where the desired accuracy of an estimated peak is a small fraction of the sampling period of the function. For example, this approach may be implemented in applications such as the location of mobiles within a cellular system.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.
The invention, together with further objects and attendant advantages, will best be understood by reference to the following detailed description, taken in conjunction with the accompanying drawings.